Start from the zero-ontology premise in its strongest form: the total information content of the universal state is exactly zero, where information means distinguishability — the capacity to rule out possibilities. The universal state Ψ is the unique state that rules out nothing. The derivation then proceeds as a chain of forced steps: each stage of quantum gravity is the minimal structure required to keep the global ledger at zero (Pearce, "The universe cancels itself out to zero", Pearce, "Some Puzzling Coincidences").
Step 1: Zero information forces quantum kinematics
A classical world cannot have zero information: any classical fact is an uncancelled distinction, so I_total > 0. Exact cancellation requires a formalism in which contents can subtract. Classical probabilities can't do this — they add positively. Complex amplitudes can: two indistinguishable-in-principle alternatives with amplitudes a and −a contribute nothing. So the superposition principle is not an empirical accident but the unique mechanism a zero ontology can use. The kinematics of reality must be Hilbert-space quantum mechanics with the universal state a single pure entangled superposition of all possible configurations (Pearce).
Two corollaries follow immediately:
No collapse. Wavefunction reduction creates a fact — a pointer of positive information ex nihilo. In a zero ontology the dynamics must be exactly unitary (Everett). Objective-collapse theories are thereby ruled out a priori, including gravitationally induced collapse à la Penrose–Diósi.
Maximal symmetry. Zero information means no preferred basis, frame, direction, origin, or moment. Ψ must be invariant under the full symmetry group of the theory — i.e., it must carry the trivial representation. Every generator of the symmetry group annihilates the state.
Step 2: The invariance constraints are gravity
The generators annihilating Ψ are precisely the constraint equations of a closed universe. Charges annihilating the state are Gauss constraints (zero total charge, colour, momentum). And a specific spacetime geometry would itself be information — a distinguished fact. So the symmetry group must include spacetime diffeomorphisms, which forces the Hamiltonian of the universe to be a constraint rather than an evolution generator:
Ĥ Ψ = 0 — the Wheeler–DeWitt equation.
This is the zero-ontology condition in dynamical form. A closed universe's total Hamiltonian vanishes identically in general relativity — not as an accident but structurally, because energy generates time translation and a zero-information universe has no external time parameter to translate along. The classical shadow of this is the zero-energy universe: positive matter/Λ energy exactly offset by negative gravitational binding energy. Gravity is thereby derived, not assumed: it is the unique long-range, unscreenable, always-attractive field whose constraint algebra closes on the total energy. Gravity is the bookkeeping device of the cancellation — the ledger that guarantees every local surplus is globally offset. A zero ontology cannot be non-gravitational.
Step 3: Kinematics of the ledger — holography
Local observers indisputably register nonzero information (memories, records). In a globally zero state, every local surplus must be exactly compensated — and the compensating structure is entanglement with the rest of the universe. Spacetime is then the representation of this entanglement web, which is exactly the modern entanglement-geometry program: the Ryu–Takayanagi relation ties areas to entanglement entropy, and dialling entanglement to zero disconnects space. The zero ontology predicts this correspondence — the "emptiness" of empty space is the cancellation being nearly exact in quasi-classical branches.
Holographic entropy bounds then follow as consistency conditions on the ledger: the maximal information a region can balance against its exterior scales with the area of the boundary — the boundary is the cancellation membrane between interior surplus and exterior deficit. This selects holographic quantum gravity, and in fact holography can be derived directly from the Wheeler–DeWitt equation itself, with the WDW equation also simplifying markedly when foliated by the null surfaces where the bookkeeping lives (Raju et al., "Holography from the Wheeler–DeWitt equation", Mehta, WDW in null-foliated spacetimes, Raju et al., "Holography of information in de Sitter space").
Independent support for the template: recent work derives the quantum-corrected Einstein equations from how quantum states are organized and distinguished — curvature as the structure that keeps the information accounts consistent (Leipzig group, EurekAlert).
Step 4: Dynamics — frozen constraint, emergent time
The theory is fundamentally timeless: ĤΨ = 0 admits no external time evolution. What we call dynamics is internal correlation — conditionalization in the Page–Wootters sense: "evolution" is the clock subsystem's entanglement with the rest within the frozen state. Everett branching supplies quasi-classical histories via decoherence; in the great majority of branches the cancellation is only approximate, and the residue is exactly what we perceive as quantum indeterminacy, interference, and EPR nonlocality (Pearce/Schwindt via Qualia Computing — "nothing happens in the universe of the Everett interpretation").
In path-integral form, the zero-ontology wavefunction of the universe is the sum over all closed, boundaryless histories — the Hartle–Hawking no-boundary amplitude, the least-information proposal, whose dominant semiclassical branch is approximately de Sitter.
The resulting theory, stated
A timeless, strictly unitary, holographically implemented Wheeler–DeWitt quantum cosmology — kinematically canonical quantum gravity (with its LQG-style discrete area spectrum as the minimal ledger entry: one quantum of area is the smallest unit of cancellation bookkeeping), with spacetime locality emerging from entanglement. Its distinctive zero-ontological commitments:
Exact unitarity, forever. No objective or gravitationally induced collapse; superpositions hold at all scales, including observers.
All conserved totals vanish identically — charge, momentum, angular momentum, and energy, with Λ counted in the sum.
Black hole information is never destroyed — the information paradox must dissolve holographically, since non-conservation would break the ledger.
Holographic bounds are fundamental, saturated by horizons; the universe's degrees of freedom scale with the cosmic horizon area, and a zero-information prior favours a small effective Λ.
Time is not fundamental — only the zero-eigenvalue constraint is.
Falsifiability and honesty
The derivation is forced only given the postulate, and the postulate's "theory" remains a sketch, as you yourself have acknowledged (Witherall, "The Zero Ontology — David Pearce on Why Anything Exists"). But it is refutable: any demonstrated fundamental collapse (e.g., intrinsic decoherence scaling with mass, as Penrose predicts), any exact global symmetry breaking, or any confirmed information non-conservation would kill it — while each extension of interference experiments to more massive, more persistent superpositions corroborates it. Crucially, the zero ontology makes quantum gravity mandatory rather than optional: a non-gravitational quantum universe would have a nonzero ledger, and that — on this framework — is the one thing that cannot exist.
Oct 26, 5:41am
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